Simultaneous large deviations for the shape of Young diagrams associated with random words

We investigate the large deviations of the shape of the random RSK Young diagrams associated with a random word of size $n$ whose letters are independently drawn from an alphabet of size $m=m(n)$. When the letters are drawn uniformly and when both $n$ and $m$ converge together to infinity, $m$ not growing too fast with respect to $n$, the large deviations of the shape of the Young diagrams are shown to be the same as that of the spectrum of the traceless GUE. In the non-uniform case, a control of both highest probabilities will ensure that the length of the top row of the diagram satisfies a large deviation principle. In either case, both speeds and rate functions are identified. To complete our study, non-asymptotic concentration bounds for the length of the top row of the diagrams, that is, for the length of the longest increasing subsequence of the random word are also given for both models.Comment: Published at http://dx.doi.org/10.3150/14-BEJ612 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

A proposal for detecting the spin of a single electron in superfluid helium

The electron bubble in superfluid helium has two degrees of freedom that may offer exceptionally low dissipation: the electron's spin and the bubble's motion. If these degrees of freedom can be read out and controlled with sufficient sensitivity, they would provide a novel platform for realizing a range of quantum technologies and for exploring open questions in the physics of superfluid helium. Here we propose a practical scheme for accomplishing this by trapping an electron bubble inside a superfluid-filled opto-acoustic cavity.Comment: Main text: 5 pages, 5 figures. Supplement: 11 pages, 2 figures, 1 tabl

Polarization engineering of entangled photons from a lithium niobate nonlinear metasurface

Complex polarization states of photon pairs are indispensable in various quantum technologies. Conventional methods for preparing desired two-photon polarization states are realized through bulky nonlinear crystals, which can restrict the versatility and tunability of the generated quantum states due to the fixed crystal nonlinear susceptibility. Here we present a solution using a nonlinear metasurface incorporating multiplexed silica metagratings on a lithium niobate film of 300 nanometer thickness. We fabricate two orthogonal metagratings on a single substrate with an identical resonant wavelength, thereby enabling the spectral indistinguishability of the emitted photons, and demonstrate in experiments that the two-photon polarization states can be shaped by the metagrating orientation. Leveraging this essential property, we formulate a theoretical approach for generating arbitrary polarization-entangled qutrit states by combining three metagratings on a single metasurface, allowing the encoding of desired quantum states or information. Our findings enable miniaturized optically controlled quantum devices using ultrathin metasurfaces as polarization-entangled photon sources.Comment: 21 pages, 5 figures, journal pape

The effect of metformin usage on survival outcomes for hepatocellular carcinoma patients with type 2 diabetes mellitus after curative therapy

ObjectiveMetformin has attracted more attention from researchers for its newly discovered antitumor effects. A meta-analysis was performed to reveal the efficacy of metformin on overall survival (OS) and recurrence-free survival (RFS) for HCC patients with type 2 diabetes mellitus (T2DM) after curative treatment.MethodsDatabases including PubMed, the Cochrane Library, Web of Science, CNKI, Wangfang, and Weipu Database up until 31 May 2022 were searched for relevant studies. STATA 13.0 was used to perform the meta-analysis.ResultsA total of six studies involving 5,936 patients were included in our study. The results from the current study revealed that metformin usage can significantly prolong the 3-year [odds ratio (OR) = 1.50, 95% confidence interval (CI): 1.22–1.83, p = 0.000] and 5-year (OR = 1.88, 95% CI: 1.47–2.41, p = 0.000) OS and decrease the 1-year (OR = 1.31, 95% CI: 1.08–1.59, p = 0.007), 3-year (OR = 1.88, 95% CI: 1.48–2.37, p = 0.000), and 5-year (OR = 1.83, 95% CI: 1.40–2.40, p = 0.000) recurrence rates.ConclusionMetformin treatment significantly prolongs the OS and decreases the recurrence rate for HCC patients with T2DM after curative HCC therapy

Related-Key Differential Attack on Round Reduced RECTANGLE-80

RECTANGLE is a newly proposed lightweight block cipher which allows fast implementations for multiple platforms by using bit-slice techniques. It is an iterative 25-round SPN block cipher with a 64-bit block size and a 80-bit or 128-bit key size. Until now, the results on analyzing the cipher are not too much, which includes an attack on the 18-round reduced version proposed by the designers themselves. In this paper, we find all 15-round differential characteristics with 26--30 active S-boxes for given input, output and round subkey differences, which have a total probability $2^{-60.5}$. Based on these differential characteristics, we extend the corresponding distinguisher to 2 rounds backward and forward respectively, and propose an attack on the 19-round reduced RECTANGLE-80 with data complexity of $2^{62}$ plaintexts, time complexity of about $2^{67.42}$ encryptions and memory complexity of $2^{72}$. TThese data and time complexities are much lower than that of the designers for the 18-round reduced RECTANGLE-80

Spatially entangled photon-pairs from lithium niobate nonlocal metasurfaces

Metasurfaces consisting of nano-scale structures are underpinning new physical principles for the creation and shaping of quantum states of light. Multi-photon states that are entangled in spatial or angular domains are an essential resource for quantum imaging and sensing applications, however their production traditionally relies on bulky nonlinear crystals. We predict and demonstrate experimentally the generation of spatially entangled photon pairs through spontaneous parametric down-conversion from a metasurface incorporating a nonlinear thin film of lithium niobate. This is achieved through nonlocal resonances with tailored angular dispersion mediated by an integrated silica meta-grating, enabling control of the emission pattern and associated quantum states of photon pairs by designing the grating profile and tuning the pump frequency. We measure the correlations of photon positions and identify their spatial anti-bunching through violation of the classical Cauchy-Schwartz inequality, witnessing the presence of multi-mode entanglement. Simultaneously, the photon-pair rate is strongly enhanced by 450 times as compared to unpatterned films due to high-quality-factor metasurface resonances, and the coincidence to accidental ratio reaches 5000. These results pave the way to miniaturization of various quantum devices by incorporating ultra-thin metasurfaces functioning as room-temperature sources of quantum-entangled photons

Dynamics and Stability of an Optically Levitated Mirror

We analyse the dynamics of a one-dimensional vertical Fabry-P\'erot cavity, where the upper mirror levitates due to intra-cavity radiation pressure force. A perturbative approach is used based around separation of timescales, which allows us to calculate the physical quantities of interest. Due to the dynamics of the cavity field, we find that the upper mirror's motion will always be unstable for levitation performed using only a single laser. Stability can be achieved for two lasers, where one provides the trapping potential and the other a damping effect, and we locate and characterise all parameter regimes where this can occur. Finally we analyse photothermal effects due to heating of the mirror substrate. We show that this can stabilise the system, even with only a single input laser, if it acts to increase the optical path length of the cavity. This work serves as a foundation for understanding how levitated optical cavity schemes can be used as stable metrological platforms.Comment: 14 pages, 7 figures. Code & data available for download at github.com/ruvilecamwasam/lmdynamic

Improved Differential Analysis of Block Cipher PRIDE

In CRYPTO 2014 Albrecht \emph{et al.} brought in a 20-round iterative lightweight block cipher PRIDE which is based on a good linear layer for achieving a tradeoff between security and efficiency. A recent analysis is presented by Zhao \emph{et al.}. Inspired by their work, we use an automatic search method to find out 56 iterative differential characteristics of PRIDE, containing 24 1-round iterative characteristics, based on three of them we construct a 15-round differential and perform a differential attack on the 19-round PRIDE, with data, time and memory complexity of $2^{62}$, $2^{63}$ and $2^{71}$ respectively